A novel pressure-exchange ejector is disclosed whereby a high energy primary fluid transports and pressurizes a lower energy secondary fluid through direct fluid-fluid momentum exchange. The pressure-exchange ejector utilizes non-steady flow principles and both supersonic flow and subsonic flow embodiments are disclosed. The invention provides an ejector-compressor/pump which can attain substantially higher adiabatic efficiencies than conventional ejectors while retaining much of the simplicity of construction and the low manufacturing cost of a conventional ejector. Embodiments are shown which are appropriate for gas compression applications such as are found in ejector refrigeration, fuel cell pressurization, water desalinization, and power generation topping cycles, and for liquid pumping applications such as marine jet propulsion and slurry pumping.